Some 500 soldiers have now been brought in to deal with "unprecedented" flooding in Yorkshire and Lancashire.
A thousand more are on stand-by after David Cameron vowed to help people in "their hour of need".
Rescuers have been evacuating homes in York where water levels are still rising, and thousands of people in north-west England are without power.
There are scores of flood warnings in England, Wales and Scotland - more than 25 severe, meaning danger to life.
On Sunday, the government said it was deploying a further 200 soldiers to affected areas on top of the 300 who were already on the ground.
After chairing an emergency conference call of the government's emergency committee Cobra, the prime minister said the "level of the rivers plus the level of rainfall has created an unprecedented effect, and so some very serious flooding".
"We will do everything we can to help people in this, their hour of need," added Mr Cameron, who is expected to visit some of the flood-affected areas on Monday.
It said about 500 properties were directly affected by flooding and a second rest centre was being opened for residents.
Meanwhile, North Yorkshire Police is urging people not to travel to flooded parts of York, as well as the Selby area, where the Ouse has burst its banks and is threatening homes in the village of Cawood.
Leeds has also been badly affected, with 1,000 homes flooded, but the city's council leader said the government had been warned "a major flood... was a catastrophe waiting to happen".
"While now is the time to focus on the wellbeing of our residents and the condition of their properties and possessions, we will again be calling on the government for further significant investment in additional flood defences," Judith Blake added.
Downing Street said emergency financial assistance would available to homes and businesses in Yorkshire and Lancashire, and they would have access to the support package announced earlier in the month for people affected by Storm Desmond in Cumbria.
Flood-damaged infrastructure - including the A591 through the heart of the Lake District - will be repaired using £40m in emergency government funding, said Transport Secretary Patrick McLoughlin.
BBC Weather forecaster Alex Deakin said affected areas had enjoyed drier conditions on Sunday.
Dry and mild conditions will follow at the start of the week, although there is the potential for more stormy weather on Wednesday.
Electricity North West said it had now reconnected 23,000 homes since Saturday but 3,000 properties may be without power until Monday. It urged people in Rochdale, the worst-hit area, to turn off Christmas lights to help save electricity.
In other developments:
- The Met Office has an amber "be prepared" weather warning in place for heavy rain for central and southern Scotland on Wednesday
- Flooding has affected phone lines in York, including the non-emergency police number 101. People are advised to call 01609 768 182 instead
- Police say West Yorkshire is experiencing its worst flooding in 70 years with more than 2,000 homes in Calderdale
- Police say the flood operation in Greater Manchester has now turned to "a recovery" phase, as water levels begin to drop
- North Yorkshire Police said they had run out of "road closed" signs
- The Conwy Valley rail route in north Wales could remain closed for several days after heavy rain caused flooding
In York, officials said pumps at the Foss Barrier - where the River Foss joins the River Ouse - had been overwhelmed and flood barriers had to be lifted, meaning areas of the city that would usually be protected were left vulnerable.
A man waiting to be evacuated from his home in York said: "It is really alarming. The whole of town is flooded, it is really extreme - I've never seen anything like this."
Leeds Central MP Hilary Benn told the BBC the flooding was the worst he had ever seen in the centre of the city. The former Labour environment secretary called for increased investment, saying climate change was bringing wetter winters.
Environment Secretary Liz Truss said the government would review flood defences which had been "overwhelmed".
Timeline: December flooding
5 December: Storm Desmond brings more than a month's rain to parts of Cumbria, leading to flooding in Carlisle and other areas
12 December: River levels remain high and more than 70 flood warnings are issued amid more heavy rain
22 December: Communities in Cumbria flood again - some for the third time in less than a month
25 December: More than 100 flood alerts and warnings are issued across England and Wales as Storm Eva brings torrential rain
26 December: Residents in West Yorkshire and Lancashire are evacuated from their homes and flooding hits Leeds, Greater Manchester and York
27 December: Police in York advise hundreds of people to evacuate their homes as 24 severe flood warnings remain in place in the north east of England
People can access information from council websites and the Environment Agency Floodline.
The agency is also operating a phone line - 0345 988 1188 - which will be staffed rather than offering recorded information.
Live flood warnings from the Environment Agency and the Scottish Environment Protection Agency.
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